Sweet Trims are made of Threes: A c\`adl\`ag erasure of the Brownian tree
Alessandra Caraceni, Nicolas Curien, William Fleurat, Adrianus Twigt

TL;DR
The paper introduces a trimming algorithm for binary trees that produces a cdle0g erasure of Brownian trees, linking combinatorial tree processes with continuous stochastic limits.
Contribution
It presents a novel simple trimming procedure that connects discrete binary trees with their continuous Brownian tree limits through a cdle0g erasure.
Findings
The trimming algorithm generates nested binary trees via leaf removal.
Its scaling limit yields a cdle0g erasure of Brownian trees.
The process relates to SLE theory and known coupling methods.
Abstract
We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer coupling, its scaling limit provides a suprising c\`adl\`ag erasure of Brownian trees, reminiscent of SLE theory.
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